Givens Rotation: Find J(2,3) and Prove Orthogonality

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Homework Help Overview

The problem involves Givens rotations, specifically finding the rotation matrix J(2,3) that transforms a given vector x = [1,-1,3]T such that the third element of the resulting vector is zero. Additionally, the task includes proving that the matrix J(2,3) is orthogonal.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the meaning of J(2,3) and whether it refers to a matrix of specific dimensions. There is an inquiry into the requirements for finding the rotation matrix and the implications of orthogonality.

Discussion Status

The discussion is ongoing, with some participants seeking clarification on the problem's requirements while others appear to be progressing toward a solution. There is no explicit consensus yet, but the exploration of concepts is active.

Contextual Notes

Participants are navigating the definitions and properties of Givens rotations, particularly in relation to the dimensions of the matrix and the conditions for orthogonality. There may be assumptions about the properties of rotation matrices that are being examined.

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Homework Statement


A Givens rotation is a matrix J(i,k) that is the identity matrix except jii = jkk = c and jik = -jki = s where c2 + s2 = 1. Let x = [1,-1,3]T. Find the rotation matrix J(2,3) such that the third element of Jx is zero. Show that J(2,3) is orthogonal.

Homework Equations


To prove orthogonality just show JTJ = I


The Attempt at a Solution

 
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What does it mean when you have to find J(2,3)? Does it mean a 2 x 3 matrix?
 
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